Thermal Expansion Converter
Convert a coefficient of thermal expansion between per kelvin, per degree Celsius, per degree Fahrenheit, per degree Rankine and per degree Réaumur. Enter the coefficient, choose the two temperature scales and read the result instantly.
Select two units to see the conversion factor.
The coefficient keeps its kind: a linear coefficient stays linear, an area coefficient stays area, a volume coefficient stays volumetric. The converter only changes the temperature degree, so it never turns one kind into another.
Thermal Expansion Formula
A coefficient of thermal expansion α is a fractional change per degree: α = (ΔL ÷ L) ÷ ΔT. It is a reciprocal temperature unit, so a smaller degree gives a smaller coefficient. Because 1 K = 1 °C = 1.8 °F = 1.8 °R = 0.8 °Ré, the coefficient per °F is the coefficient per °C divided by 1.8. Result = value × (source factor ÷ target factor), with factors measured in 1/K.
What Is the Coefficient of Thermal Expansion?
When a material is heated it usually expands. The coefficient of thermal expansion says by what fraction. The linear coefficient α gives the relative change in length per degree: ΔL = α × L × ΔT. Steel is about 12 × 10⁻⁶ per °C, which means a 1 m bar grows by about 0.012 mm for each degree of warming.
There are three related coefficients: linear (length), area (about 2α for an isotropic solid) and volumetric (about 3α). They are different numbers for the same material. This converter does not convert between the three. The units on the page, such as 1/K, only describe the temperature degree; whether your number is linear, area or volumetric stays as you entered it.
The unit is a reciprocal temperature. A Fahrenheit degree is smaller than a Celsius degree (1 °C = 1.8 °F), so the same material has a coefficient 1.8 times smaller when expressed per °F. The conversion uses temperature intervals only, so no 32 or 273.15 offsets are involved. See also the Temperature Interval Converter.
Coefficients can be negative: water contracts when it warms between 0 °C and about 4 °C and some materials, such as certain ceramics, shrink on heating. That is why this converter accepts negative values.
Supported Units
This converter supports the following 5 units, all for a coefficient per temperature degree. The last column gives the value of the unit in 1/K.
| Unit | Symbol | Value in 1/K |
|---|---|---|
| Length per length per kelvin | 1/K | 1 |
| Length per length per degree Celsius | 1/°C | 1 |
| Length per length per degree Fahrenheit | 1/°F | 1.8 |
| Length per length per degree Rankine | 1/°R | 1.8 |
| Length per length per degree Réaumur | 1/°Ré | 0.8 |
How to Use the Thermal Expansion Converter
- Type the expansion coefficient in the value box. Decimals and scientific notation such as 0.0025 or 2.5e-3 are accepted.
- Choose the From unit and the To unit.
- The result appears instantly, or press Convert Now. Very large or very small results are shown in scientific notation.
- Use Swap Units to reverse the conversion, Copy Result to copy the answer, open Show this value in all units for a full list, and Clear to start again.
Step-by-step by hand
- Find the size of each unit in the common base unit (1/K): 1 1/°C = 1 1/K and 1 1/°F = 1.8 1/K.
- Divide the source size by the target size to get the conversion factor: 1 ÷ 1.8 = 0.5555555556, so 1 1/°C = 0.5555555556 1/°F.
- Multiply by your value: 1.2e-5 1/°C × 0.5555555556 = 6.666666667e-6 1/°F.
Negative coefficients are accepted. Remember that a linear coefficient stays linear after conversion.
Common Thermal Expansion Conversions
- Steel: 0.000012 per °C equals 6.666666667e-6 per °F.
- Aluminium: 0.000023 per K equals 1.277777778e-5 per °F.
- Imperial to metric: 0.000006 per °F equals 1.08e-5 per °C.
- Rankine: 0.000005 per °R equals 9e-6 per K.
- Réaumur: 0.00001 per °Ré equals 8e-6 per °C.
- Negative coefficient: −0.00002 per K equals -1.111111111e-5 per °F.
Per °C to Per °F – Common Values
Quick reference for frequently used values
| 1/°C | 1/°F | 1/K | 1/°Ré |
|---|---|---|---|
| 1e-6 | 5.555555556e-7 | 1e-6 | 1.25e-6 |
| 5e-6 | 2.777777778e-6 | 5e-6 | 6.25e-6 |
| 1e-5 | 5.555555556e-6 | 1e-5 | 1.25e-5 |
| 1.2e-5 | 6.666666667e-6 | 1.2e-5 | 1.5e-5 |
| 2.3e-5 | 1.277777778e-5 | 2.3e-5 | 2.875e-5 |
| 0.0001 | 5.555555556e-5 | 0.0001 | 0.000125 |
Where and Why This Conversion Is Used
- Mechanical and civil engineering: expansion joints, rails, pipes and bridges.
- Precision instruments: thermal drift of optical and measuring parts.
- Materials data: tables are published per °C, per K or per °F.
- Electronics: matching expansion of chips, solder and boards.
Limitations
- Linear, area and volumetric coefficients are different quantities; a ppm/K figure is a linear, area or volumetric value only according to its source.
- The coefficient is treated as constant over the temperature range, which holds only approximately.
- Strictly a unit conversion of the degree: it does not estimate how much a part will expand.
Important Differences Between Related Heat Quantities
- Specific heat capacity, J/(kg·K): energy needed to warm one kilogram of a material by one kelvin. It is not the total heat capacity of an object (J/K), which also depends on how much material there is, and it is not molar heat capacity (J/(mol·K)).
- Heat density, J/m²: heat or radiant energy delivered per unit area over a period. Heat flux density, W/m² is the rate of that transfer, energy per area per time. They are not interchangeable.
- Heat flux density, W/m² is heat flow per area. The heat transfer coefficient, W/(m²·K) is heat flux per kelvin of temperature difference, so heat flux = coefficient × temperature difference.
- Thermal conductivity, W/(m·K) is a material property. The heat transfer coefficient is a property of a surface or an assembly, and thermal resistance, K/W belongs to one specific object. Resistance is not conductivity or resistivity: R = L ÷ (k × A) for a slab.
- Temperature interval vs temperature: a difference of 10 °C is a difference of 18 °F. A reading of 10 °C is 50 °F. Every unit here that contains “per degree” or “K” uses intervals, so no offset is ever applied.
Each converter changes units within one quantity only. Related tools: Temperature Interval, Thermal Expansion, Thermal Resistance, Thermal Conductivity, Specific Heat Capacity, Heat Density, Heat Flux Density, Heat Transfer Coefficient, Fuel Efficiency - Mass and Fuel Efficiency - Volume.